/sci/ - Science & Math

>>9814848
that's like studying literature without learning how to read.

Not the hardest problem I know, but one I doubt you can Google or Wolframalpha an answer for.

Consider a 2D scalar field [math]E[/math] obeying the Helmholtz equation:

[math]\nabla^2 E(\vec{r}) + k^2 E(\vec{r}) = j\omega \mu J(\vec{r})[/math]

where

[math]k^2 = \omega^2 \mu_0 \epsilon(\vec{r})[/math],

where [math]k[/math] is wavenumber, [math]\omega[/math] is frequency, [math]\mu_0[/math] is a constant, [math]\epsilon[/math] is a function space, and [math]J[/math] is a source term

Integrating this, we can reformulate the equation as

[math]E(\vec{r}) = E^{(i)}(\vec{r}) + k^2 \int_{A^\prime} E(\vec{r}^\prime) \chi(\vec{r}^\prime) G(\vec{r},\vec{r}^\prime) dA^\prime[/math]

or

[math]E(\vec{r}) = E^{(i)}(\vec{r}) + E^{(s)}(\vec{r})[/math]

Where [math]E[/math] is the total field, [math]E^{(i)}[/math] is an incident field, [math]\chi = \frac{\epsilon}{\epsilon_0} - 1[/math] is contrast, and [math]G(\vec{r},\vec{r}^\prime) = \frac{1}{j4}H_0^{(2)}(k|\vec{r} - \vec{r}^\prime|)[/math] is the 2D Green's function associated with the PDE.

Assume you have an object that determines an unknown [math]\epsilon[/math] that you probe with incident field [math]E^{(i)}[/math]. Given a finite number of point measurements of the scattered field [math]E^{(s)}[/math], solve for the [math]\epsilon[/math].

This is simple. You should be able to do this.

>>8817870
>So i come to you to disprove that earth is flat
I can't disprove something if you make no concrete claims (ie equations). Make a concrete claim, and we can explore that claim, it's consequences, and see if it matches observation.

You know, science.

My claim is that the classical theory of gravity using only Netwon's law

[math]\vec{F} = m \vec{a}[/math]

and the classical gravity force law

[math]\vec{F} = G \frac{m M}{R}\hat {R}[/math]

Is sufficient to describe mechnics of not only the motion of the earth and sun relative to each other, but also the motion of all bodies in the solar system to good accuracy.

Now it's your turn to make some concrete claims.